Component 512: Linear Valve with Pneumatic Actuator by HVACSIM+ General Description A valve is essentially a variable fluid resistance. The manner in which the flow rate varies with valve stem position is known as the valve characteristic, or inherent characteristic, since it is always measure in practice with a constant pressure drop across the valve. For a linear valve, the flow rate is directly proportional to the valve stem position when the pressure drop across the valve is constant. It is important to distinguish between the inherent characteristic of a valve and the installed characteristic. The latter depends on both the inherent characteristic and the authority of the valve (as discussed in section 4.0 of reference [1]). The installed characteristic of an inherently linear valve is strictly linear only when the authority is one, that is, when the valve represents the only pressure drop in the system. A valve with low authority has little effect on the flow rate over most of its operating range. When used in a system with other component models, the Component 512 valve accurately models the effects of valve authority. The valve model includes a pneumatic actuator model. Actuator hysteresis is represented using the utility subroutine HYSTER (described in section 3.2 of reference [1]). The dynamic response of the actuator is modeled by a first order differential equation. The actuator can be effectively removed by setting the time constant and the hysteresis parameter to zero. When the flow rate through the valve goes to zero, the pressure drop across the valve becomes indeterminate. To prevent this problem, a non-zero leakage parameter is required by the model. Nomenclature C - requested relative valve position (0 <= C <= 1) Ca - relative actuator position (0 <= Ca <= 1) Ch - relative valve position (0 <= Ch <= 1) hys - fraction of actuator's range over which Ch remains constant when actuator's direction of travel reverses K - flow resistance parameter when valve is open (Ch = 1) w - mass flow rate y - leakage parameter: fractional leakage when DeltaP = 1. Toll - actuator time constant Mathematical Description The relationship between the input control signal, C, and the actuator position, Ca, is defined by: d(Ca)/dt = (C - Ca)/Toll This differential equation is solved by MODSIM, the main HVACSIM+ program, unless the time constant, Toll, is less than one second, in which case the following solution is used: IF (Toll/DeltaT) < 0.05 OR | Css - C- | < 10^(-10) THEN Ca = Css ELSE Ca = C - (C - Ca-)*exp(-DeltaT/Toll) where Ca- is the value of Ca one time step ago. The actuator position differs from the valve position, Ch, due to hysteresis effects, which are determined by the utility function HYSTER (described in section 3.2 of reference [1]). Ch = HYSTER(Ca,hys) The inlet pressure is given by Pi = Po + sign(w)*K*w^2*[(1 - y)*Ch + y]^(-2) Component 512 Configuration Inputs Description 1 Po - pressure at outlet 2 w - mass flow rate 3 C - input control signal (0 <= C <= 1) 4 Ca - actuator relative position Outputs Description 1 Ca - actuator relative position 2 Pi - pressure at inlet Parameters Description 1 K - flow resistance when valve is open 2 Toll - actuator time constant 3 y - leakage parameter 4 hys - hysteresis parameter Reference: 1. HVACSIM+ Building Systems and Equipment Simulation Program Reference Manual (NBSIR 84-2996) Daniel R. Clark United States Department of Commerce National Institute of Standards and Technology Gaithersburg, Maryland 20899-0001